A spatiotemporal model can be viewed either as a temporally varying spatial model or as spatially varying time series model [1]}. In either case, the data modeled is assumed to be characterized by both spatial and temporal dependencies. In contrast, in multivariate models, we relax the stationarity assumption that allows us to model the sequential dependencies in the temporal dimension. Instead, we assume that the observations are exchangeable in their joint distribution. Exchangability give us the following factorization.
\(p\big (\left(\mathbf {y}_1,\mathbf {x}_1\right), \cdots ,\left(\mathbf {y}_N, \mathbf {x}_N\right), \theta \big )= \prod _{n=1}^N p\big (\left(\mathbf {y}_n,\mathbf {x}_n\right)\mid \theta \big )p(\theta )\) 
